"privilege" is a form of social power and/or cultural capital. Sometimes it's derived from being part of a social majority or sometimes, in hierarchical social systems, from x having more culturally-enforced social power-over than y because of a physically unrelated but culturally sanctioned z.

I'm sure there are better/simpler definitions if you google, but mine would obviously be based in ethical philosophy and I presume you want to reach your own working definition anyway.

(Note: I'm reasonably attached to concepts of "power-over" and "power-with", i.e. I have power-with you and you have power-with me because we have mutually chosen a relationship but someone would have power-over us if they could impose their choice of relationship terms on us without our consent.)